My lexmark 5600 series does not want to switch on. power cable is connected and plugged into a working outlet.

hi Jane.
go to this link its the manual should help you out.
Lexmark 5600 Series User Manual How Are Ip Addresses Assigned
or this link might be of help to you.
What is the IP address of Lexmark printer 5600 series Google Search

1 Press to turn the printer off. 2 Disconnect the power cord from the wall outlet. 3 Gently remove the power supply from the printer. 4 Reconnect the power supply to the printer. 5 Plug the power cord into the wall outlet. 6 Press to turn the printer on.
Make sure the cord on the back of the printer is pushed all the way into the socket, it should only fit one way. If that fails, check that there is power at the outlet you are using.

Try pressing the power a little longer for the printer to start.

This issue may be due to one of the following:

• An incorrectly set power switch.
  
• An improperly functioning power outlet, surge protector, or power supply backup.
  
• A poorly connected power or data cable.
  
• A defect with a third-party (i.e. non-Lexmark) option such as a memory card.
  
• An incorrectly connected or malfunctioning optional paper tray.
  
• A malfunctioning printer component.

Please try the following steps:

Step Action 1 Make sure the power switch is in the "on" position. If it is, power off the printer. 2 If your printer's power cord is plugged into a surge protector or uninterruptible power supply (UPS), unplug it and connect it directly to a grounded wall outlet. Some of these devices can interfere with consistent electrical flow and cause the printer to fail to power up properly. 3 Disconnect the power cord from the back of the machine and then reconnect it. Make sure the power cord is plugged in all the way. 4 Disconnect any data cables (parallel, USB, Ethernet) from the rear of the printer. Any defect in a data cable may cause an electrical short circuit that could cause a loss of power to the printer. 5 Turn the printer on, this time with only the power cord connected and plugged directly into a grounded wall outlet. 6 If the printer still fails to power up, power off the printer once more. Verify that the outlet is working properly by connecting another device to it to see if it receives power. You can also try plugging the printer into a different grounded outlet. 7 If possible, try another printer power cord. 8
Verify that the printer is the correct voltage type for the environment in which it is being used. A 110V (low-voltage) printer will not work properly in a 220V (high-voltage) environment, and vice versa.

• NOTE: Look at the rear of the printer and locate the electrical specifications sticker. Verify that the voltage rating on the sticker is the correct voltage for your printing environment (i.e. 110V or 220V).

9
Remove any third-party (i.e. non-Lexmark) options, such as memory cards, as they may interfere with proper printer functioning. Also remove any paper-handling options such as an optional second paper tray. 10
Attempt to power on the printer once more with all options removed, having verified that other devices work from that power outlet.
If there is still no power, the printer may require service to fix the issue. Please contact Lexmark Technical Support or a local service provider.

Try to unplug the power adapter from the printer.


Then unplug the power cord from the power outlet. Wait at least 10 seconds before re-plugging the power cord into the power outlet in the wall (bypass any power strip) and the power adapter into the printer. This will give enough time for the printer to reset itself. If printer won't automatically turn on, press the power button. If that doesn't help, please contact Lexmark Technical Support Center for additional assistance.

Please go through the following checklist
- Make sure the power cord is plugged in securely and directly to the power outlet. Power surge protectors can draw power away from the printer.
- Disconnect the power cord from the power outlet and the back of the printer and then reconnect it.
- Check the power supply box (if there is one) to see if it is warm or cold, as there could be a defective power supply issue.
- If there is access to a voltmeter, test the power supply to ensure that it registering the correct amount of voltage (most Lexmark printers have a 30Volt output).
- Make sure the correct power supply is connected to the printer.

Source: The Printer is Not Powering On

Unfortunately no, Lexmark does have some models that are dual voltage but not this one.

when you want to delete some print jobs command try to unplug data cable first then cancel print jobs this will sure help your query

This will help. Thanks please keep updated. please do rate the solution positively .Thank you for using Fixya

Regards
manish

You may need to run the installation software that came with your new 5600 series machine.

Turn off the printer and remove the USB cable. Uninstall the drivers in Add and Remove Programs or look in the Lexmark folder in your Start Menu for a built in uninstall program for that Lexmark. Reinstall the drivers and plug the printer back in when told. INSTALL THE DRIVERS BEFORE CONNECTING THE PRINTER There are more problems with printers than ANY other device that can be attached to a computer. Check that your USB cable isn't broken or the ports themselves on the printer and the computer. Also check in Control Panel/Printers that the Lexmark is set as your default printer.